The _Premaxillaries_ are of very peculiar shape, somewhat like a _u_, with one side--the lower--the longer. The upper portion articulates with the nasals, running along the narial opening to about three inches from the angle; the free portion is short, slender, and tapering; it is curved downwards and slightly inwards; the premaxillaries do not meet, leaving the incisive foramen unenclosed, and are edentulous. At the end of the upper portion there are prominent processes for the attachment of the muscles of the proboscis, which probably resembled that of the tapir. The anterior narial opening is very large, but is considerably concealed by the overhanging of the nasals. There is no osseous septum between the nostrils. The posterior nares are much smaller, being especially contracted in width; it is divided above by the _Vomer_, which is very short, and does not reach the palatines. The nasal cavity thus formed is long, straight, and gradually narrows backwards. Of the Mandible we have but a small portion of the right ramus, comprising the part opposed to the upper canine, from the dental canal downwards. The jaw at this place has a large downward-projecting process, very similar to that figured by Marsh in his plate of _Dinoceras laticeps_. This process curves slightly outward, and has its external side convex in both directions, and its internal side convex fore-and-aft, concave from above downwards. The posterior mental foramen, which is the only one preserved in our specimen, corresponds in size and position with _Dinoceras laticeps_. The only difference between the two is a very slight one: in _D._ the curve of the posterior margin of the process is convex; in _Uintatherium_ it is concave; the angle which the process makes with the jaw is also greater. _Cranial Measurements._